\(A_{ij}(t)\)  is the temporal adjacency matrix, which represents interactions between agents [1]}. \(A_{ij}(t)=1\)  when there is an input from agent \(j\)  to \(i\)  and \(A_{ij}(t)=0\)  otherwise. If an agent with a set activity level \(a_i \in [\varepsilon , 1]\)  is active at time \(t\) , then they will interact with \(m\)  other agents, weighted by the probability \(p_{ij}\)  that agent \(i\)  would connect with agent \(j\) . These interactions are captured by the temporal adjacency matrix. The probabilistic reciprocity factor \(r \in [0, 1]\)  determines the chance that a connection is mutually influential, \((A_{ij}(t)=A_{ji}(t)=1)\) . If the interaction is reciprocated, both agents update their opinions; otherwise, only one of the agents' opinions is updated.
